SRC/dgeqp3.f(3)

NAME
SRC/dgeqp3.f

SYNOPSIS

  Functions/Subroutines
subroutine dgeqp3 (m, n, a, lda, jpvt, tau, work, lwork, info)
DGEQP3

Function/Subroutine Documentation

  subroutine dgeqp3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DGEQP3

Purpose:

    !>
    !> DGEQP3 computes a QR factorization with column pivoting of a
    !> matrix A:  A*P = Q*R  using Level 3 BLAS.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, the upper triangle of the array contains the
    !>          min(M,N)-by-N upper trapezoidal matrix R; the elements below
    !>          the diagonal, together with the array TAU, represent the
    !>          orthogonal matrix Q as a product of min(M,N) elementary
    !>          reflectors.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,M).
    !>

    JPVT

    !>          JPVT is INTEGER array, dimension (N)
    !>          On entry, if JPVT(J).ne.0, the J-th column of A is permuted
    !>          to the front of A*P (a leading column); if JPVT(J)=0,
    !>          the J-th column of A is a free column.
    !>          On exit, if JPVT(J)=K, then the J-th column of A*P was the
    !>          the K-th column of A.
    !>

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO=0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 3*N+1.
    !>          For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
    !>          is the optimal blocksize.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit.
    !>          < 0: if INFO = -i, the i-th argument had an illegal value.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The matrix Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - tau * v * v**T
    !>
    !>  where tau is a real scalar, and v is a real/complex vector
    !>  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
    !>  A(i+1:m,i), and tau in TAU(i).
    !>

Contributors:
    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA

Definition at line 150 of file dgeqp3.f.

Author

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